If A = {x : x ∈ W, x < 2}, B = {x : x ∈ N, 1 < x < 5},
Question:

If A = {x : x ∈ W, x < 2}, B = {x : x ∈ N, 1 < x < 5}, C = {3, 5} find

(i) A × (B ∩ C)

(ii) A × (B ∪ C)

Solution:

According to the question,

A = {x: x ∈ W, x < 2}, B = {x : x ∈N, 1 < x < 5} C = {3, 5}; W is the set of whole numbers

A = {x: x ∈ W, x < 2} = {0, 1}

B = {x : x ∈N, 1 < x < 5} = {2, 3, 4}

(i)

(B∩C) = {2, 3, 4} ∩ {3, 5}

(B∩C) = {3}

A × (B∩C) = {0, 1} × {3} = {(0, 3), (1, 3)}

Hence, the Cartesian product = {(0, 3), (1, 3)}

(ii)

(B∪C) = {2, 3, 4} ∪ {3, 5}

(B∪C) = {2, 3, 4, 5}

A × (B∪C) = {0, 1} × {2, 3, 4, 5} = {(0, 2), (0, 3), (0, 4), (0, 5), (1, 2), (1, 3), (1, 4), (1, 5)}

Hence, the Cartesian product = {(0, 2), (0, 3), (0, 4), (0, 5), (1, 2), (1, 3), (1, 4), (1, 5)}

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